On the sharp upper and lower bounds of multiplicative Zagreb indices of graphs with connectivity at most k

2017/04/23 by Wang, Shaohui
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.06943

Abstract

For a (molecular) graph, the first multiplicative Zagreb index ∏₁(G) is the product of the square of every vertex degree, and the second multiplicative Zagreb index ∏₂(G) is the product of the products of degrees of pairs of adjacent vertices. In this paper, we explore graphs in terms of (edge) connectivity. The maximum and minimum values of ∏₁(G) and ∏₂(G) of graphs with connectivity at most k are provided. In addition, the corresponding extremal graphs are characterized, and our results extend and enrich some known conclusions.

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